A bank currently has checkable deposits of $100,000, total reserves of $30,000, and loans of $70,000. If the required reserve ratio is lowered from 20 percent to 15 percent, this bank can increase its loans by:
A) $10,000.
B) $15,000.
C) $75,000.
D) $5,000.
E) $ 0.

Question

Quizplus · Accepted Answer

We can use the formula for maximum potential change in loans to find out how much the bank can increase its loans by:

ΔLoans = ΔDeposits × (1/Required Reserve Ratio)

Initial deposits = $100,000
Initial required reserve ratio = 20% = 0.20
Initial reserves = $30,000

So, initially: 
Maximum potential change in loans = ΔDeposits × (1/Required Reserve Ratio)
= ($100,000 - $30,000) × (1/0.20)
= $70,000 × 5
= $350,000

If the required reserve ratio is lowered to 15%, then the new reserve requirement becomes:

New reserve requirement = 15% × $100,000
= $15,000

The bank already has reserves of $30,000, so it has excess reserves of:

Excess reserves = $30,000 - $15,000
= $15,000

The bank can use these excess reserves to create more loans. The maximum potential change in loans is:

ΔLoans = ΔDeposits × (1/New Required Reserve Ratio)
= ($100,000 - $30,000 + $15,000) × (1/0.15)
= $85,000 × (1/0.15)
= $566,667

So, the bank can increase its loans by:
$566,667 - $70,000 = $496,667

However, the question asks us how much the bank can increase its loans by, relative to the initial level of loans. The initial level of loans is $70,000, so the increase in loans is:

$496,667 - $70,000 = $426,667

This is not one of the options given, but the closest one is B) $15,000. This is the increase in loans that can be directly attributed to the reduction in the reserve requirement, without taking into account any other factors that may affect the bank's lending decisions.

A Bank Currently Has Checkable Deposits of $100,000, Total Reserves